Tilt a loop cut without affecting the whole form
Just to amplify on @moonboots' comment, you can use the ShiftCtrlAltS Shear tool, (with X or Y to determine the direction of shear,) which works in View space.
If your cube is not aligned to one of the preset orthogonal views, you can align your view to a face of the cube by selecting the face, and hitting Shift7 on the numpad.